The second part of this paper pursues a similar objective with respect to kinematics of moving and deforming level sets of dynamic scalar environmental fields.
This issue is inherent in dealing with the problem of robotic detection, localization, and exploration of such sets. This problem is also a subject of an extensive research; see e.g., [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, [14]}, [15]} and the literature therein. A typical relevant mission is to find and arrive at an a priori unknown level set where an environmental field assumes a specific threshold value, and then to cover the entirety of this set. This results in exhibiting and gaining control over the border of the region with greater field values, which is commonly the major focus of interest.
Examples include tracking of oil or chemical spills, or other contaminants [16]}, detection and monitoring of harmful algae blooms [11]}, tracking zones of turbulence, contaminant clouds [5]}, or high radioactivity level, exploration of sea salinity and temperature or hazardous weather conditions, to name just a few.
Up to now, the research on robotic tracking of environmental level sets mostly dealt with 2D work-spaces.
Meanwhile, expansion of underwater, flying, and space robots motivates strong interest to autonomous navigation with using all three dimensions and to cases where the problem cannot be reduced to a 2D setting. Handling these issues inevitably addresses kinematics of isosurfaces in 3D, which is the second topic of this paper.
